Abstract
A model is developed to calculate the Hall–Petch relation parameters for the submicrocrystalline (SMC) metals fabricated by severe plastic deformation (SPD) methods. The model is based on the assumption that the flow stress in SMC metals includes both conventional contributions (caused by lattice dislocations, impurity atoms, etc.) and a contribution related to the long-range internal stress fields created by the SPD-induced defects distributed over grain boundaries. Equations are derived to calculate the Hall–Petch relation parameters as functions of the strain and the strain rate. The results calculated by the derived equations agree well with the experimental data. The low resistance of grain boundaries to the motion of grain boundaries in SMC materials (see part I of this work) is found to be related to a violation of the Hall–Petch relation in SMC metals.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
V. N. Chuvil’deev, Nonequilibrium Grain Boundaries in Metals. Theory and Applications (Fizmatlit, Moscow, 2004).
V. M. Segal, I. J. Beyerlein, C. N. Tome, V. N. Chuvil’deev, and V. I. Kopylov, Fundamentals and Engineering of Severe Plastic Deformation (Nova Sci. Publ., New York, 2010).
V. N. Chuvil’deev, A. V. Nokhrin, V. I. Kopylov, Yu.G. Lopatin, N. V. Melekhin, O. E. Pirozhnikova, M. M. Myshlyaev, and N. V. Sakharov, “Conditions for the applicability of the Hall–Petch relation for nanoand microcrystalline materials produced by severe plastic deformation,” Deform. Razr. Mater., No. 12, 17–25 (2009).
A. Mishra, B. K. Kad, F. Gregori, and M. A. Meyers, “Microstructural evolution in copper subjected to severe plastic deformation: experiments and analysis,” Acta Materialia 65, 13–28 (2007).
W. Yuan, S. K. Panigrahi, J.-Q. Su, and R. S. Mishra, “Influence of grain size and texture on Hall–Petch relationship for a magnesium alloy,” Scripta Materialia 65, 994–997 (2011).
M. A. Munoz-Morris, O. C. Garcia, and D. G. Morris, “Mechanical behavior of dilute Al–Mg alloy processed by equal channel angular pressing,” Scripta Mater. 48 (3), 213–218 (2003).
E. V. Kozlov, A. M. Glezer, N. A. Koneva, N. A. Popova, and I. A. Kurzina, Fundamentals of the Plastic Deformation of Nanostructured Materials, Ed. by A. M. Glezer (Fizmatlit, Moscow, 2016).
R. A. Andrievskii and A. M. Glezer, “Size effects in nanocrystalline materials: II. Mechanical and physical properties,” Phys. Met. Metallogr. 89 (1), 85–95 (2000).
V. A. Pozdnyakov, “Mechanisms of plastic deformation and the anomalies of the Hall–Petch dependence in metallic nanocrystalline materials,” Phys. Met. Metallogr. 96 (1), 105–119 (2003).
Y. T. Zhu and T. G. Langdon, “Influence of grain size on deformation mechanisms: an extension to nanocrystalline materials,” Mater. Sci. Eng. A. 409 (1–2), 234–242 (2005).
W. J. Kim, S. I. Hong, Y. S. Kim, S. H. Min, H. T. Jeong, and J. D. Lee, “Texture development and its effect on mechanical properties of an AZ61 Mg alloy fabricated by equal channel angular pressing,” Acta Mater. 51 (11), 3293–3307 (2003).
A. Yamashita, Z. Horita, and T. G. Langdon, “Improving the mechanical properties of magnesium and magnesium alloy through severe plastic deformation,” Mater. Sci. Eng. A 300 (1–2), 142–147 (2001).
M. R. Barnett, Z. Keshavarz, A. G. Beer, and D. Atwell, “Influence of grain size on the compressive deformation of wrought Mg–3Al–1Z,” Acta Materialia 52 (17), 5093–5103 (2004).
M. I. Goldshtein, V. S. Litvinov, and B. M. Bronfin, Physical Metallurgy of High-Strength Alloys (Metallurgiya, Moscow, 1986).
J. P. Hirth and J. Lothe, Theory of Dislocations (McGraw-Hill, New York, 1967).
V. N. Chuvil’deev, O. E. Pirozhnikova, and A. V. Petryaev, “Micromechanisms of grain-boundary recovery upon annealing after deformation: I. Recovery of diffusional properties of grain boundaries,” Phys. Met. Metallogr. 92 (6), 540–545 (2001).
A. V. Petryaev and V. N. Chuvil’deev, “Micromechanisms of grain-boundary recovery upon annealing after deformation: II. Recovery of yield strength in finegrained materials,” Phys. Met. Metallogr. 92 (6), 546–552 (2001).
V. N. Chuvil’deev, A. V. Nokhrin, V. I. Kopylov, M. Yu. Gryaznov, O. E. Pirozhnikova, and Yu. G. Lopatin, “Effect of a simultaneous increase in strength and plasticity at room temperature in the nano-and microcrystalline metals fabricated by severe plastic deformation. Part I. Model for calculating the limiting strength and plasticity at room temperature,” Materialoved., No. 12, 2–10 (2010).
Y. Estrin, H. S. Kim, and F. R. N. Nabarro, “A comment on the role of Frank-Read sources in plasticity of nanomaterials,” Acta Mater. 55, 6401–6407 (2007).
V. I. Chuvil’deev, V. I. Kopylov, A. V. Nokhrin, I. M. Makarov, and Yu. G. Lopatin, “Dispersion limit for ECA deformation: effect of temperature,” Dokl. Ross. Akad. Nauk 369 (3), 332–338 (2004).
V. I. Chuvil’deev and V. I. Kopylov, “Grain refinement limit upon equal-channel angular deformation,” Russ. Metall. (Metally), No. 1, 22–35 (2004).
V. N. Perevezentsev, V. V. Rybin, and V. N. Chuvil’deev, “The theory of structurual superplastisity,” Acta Met. Mater. 40 (5), 887–923 (1992).
V. N. Chuvil’deev, “Micromechanism of grain-boundary self-diffusion in metals: II. Model of grain-boundary self-diffusion in boundaries,” Phys. Met. Metallogr. 81 (4), 387–392 (1996).
V. N. Chuvil’deev and O. E. Pirozhnikova, “Micromechanism of grain-boundary self-diffusion in metals: III. Effect of lattice dislocation fluxes on the diffusion properties of grain boundaries,” Phys. Met. Metallogr. 81 (7), 71–77 (1996).
Ultrafine Grain in Metals, Ed. by L. K. Gordienko (Metallurgiya, Moscow, 1973).
R. Z. Valiev and T.G. Langdon, “Principles of equalchannel angular pressing as a processing tool for grain refinement,” Prog. Mater. Sci. 51 (8), 881–981 (2006).
A. P. Zhilyaev and T. G. Langdon, “Using high-pressure torsion for metal processing: fundamentals and applications,” Prog. Mater. Sci. 53 (6), 893–979 (2008).
J. De Messemaeker, B. Verlinden, and J. Van Humbeeck, “On the strength of boundaries in submicron IF steel,” Mater. Lett. 58 (29), 3782 (2004).
I. Gutierrez-Urrutia, M. A. Munoz-Morris, and D. G. Morris, “Contribution of microstructural parameters to strengthening in a ultrafine-grained Al–7% Si alloy processed by severe deformation,” Acta Mater. 55, 1319–1330 (2000).
M. V. Degtyarev, T. I. Chashchukhina, L. M. Voronova, A. M. Patselov, and V. P. Pilyugin, “Influence of the relaxation processes on the structure formation in pure metals and alloys under high-pressure torsion,” Acta Mater. 55 (18), 6039–6050 (2007).
W. Wei, G. Chen, and J. Wang, “Microstructure and tensile properties of ultrafine grained copper processed by equal-channel angular pressing,” Rare Metals 25 (6), 697–703 (2006).
G. G. Frost and M. F. Eshbi, Deformation-Mechanism Maps (Pergamon, Oxford, 1982).
Author information
Authors and Affiliations
Corresponding author
Additional information
Original Russian Text © V.N. Chuvil’deev, A.V. Nokhrin, M.M. Myshlyaev, V.I. Kopylov, Yu.G. Lopatin, N.V. Melekhin, A.V. Piskunov, A.A. Bobrov, O.E. Pirozhnikova, 2018, published in Metally, 2018, No. 3, pp. 73–87.
Rights and permissions
About this article
Cite this article
Chuvil’deev, V.N., Nokhrin, A.V., Myshlyaev, M.M. et al. Effect of Recovery and Recrystallization on the Hall–Petch Relation Parameters in Submicrocrystalline Metals: II. Model for Calculating the Hall–Petch Relation Parameters. Russ. Metall. 2018, 487–499 (2018). https://doi.org/10.1134/S0036029518050051
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0036029518050051